Is there a reason in the Potterverse to use a wand?
There are many creatures that use magic without a wand, why do wizards need to use wands?
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Wands are a way to channel (or focus) your magic. As Ollivander tells Harry in HP7:
Oh yes, if you are any wizard at all you will be able to channel your magic through almost any instrument.
In addition, a properly affiliated wand reinforces your magic in a sort-of feedback loop, see that same explanation from Ollivander in terms of wandlore.
Other creatures' magic is different from Wizards, perhaps it's easier to channel/focus; or perhaps they are restricted to magic types that are wandless (JKR never expanded on that).
But wands do seem to offer even non-humans better magic scope, as evidenced by Griphook's explanation to Harry, again in Deathly Hallows:
“The right to carry a wand,” said the goblin quietly, “has long been contested between wizards and goblins.”
“Well, goblins can do magic without wands,” said Ron.
“That is immaterial! Wizards refuse to share the secrets of wandlore with other magical beings, they deny us the possibility of extending our powers!”
In his notes for “Babbitty Rabbitty and Her Cackling Stump”, Dumbledore describes wands as instruments through which magic is supposed to be channeled.
“While the “rogue” ability to perform magic sometimes appears in those of apparent non-magical descent (though several later studies have suggested that there will have been a witch or wizard somewhere on the family tree), Muggles cannot perform magic. The best — or worst — they could hope for are random and uncontrollable effects generated by a genuine magical wand, which, as an instrument through which magic is supposed to be channeled, sometimes holds residual power, which it may discharge at odd moments — see also the notes on wandlore for “The Tale of the Three Brothers.”
- The Tales of Beedle the Bard
While wizards are capable of doing magic without a wand just as non-humans are, the results of it would be less precise and less powerful than that of magic done by using a wand.
The magic wand originated in Europe. Wands channel magic so as to make its effects both more precise and more powerful, although it is generally held to be a mark of the very greatest witches and wizards that they have also been able to produce wandless magic of a very high quality. As the Native American Animagi and potion-makers demonstrated, wandless magic can attain great complexity, but Charms and Transfiguration are very difficult without one.
- History of Magic in North America, Fourteenth Century – Seventeenth Century (Pottermore)
Wands focus and channel magic, improving its effect. Non-human creatures don’t need wands to use magic, but it’s likely that they too would use wands if wizards hadn’t outlawed it, since goblins in general are very angry with wizards for not allowing them to have wands.
It is noteworthy that wizards don't need to use a wand. According to Pottermore, wands are a European invention, African wizards in particular regularly perform wandless magic; as did native American wizards.